RoofSurface temperatures of the building envelope can sometimes reach extreme values due to solar radiation, which can increase temperatures by 20 or 30 °C.  In fact, radiation from the roof to the sky can actually decrease surface temperatures.  It therefore becomes difficult to predict what temperature range to expect, unless you have lots of field experience in a given climate.

The same problem was discovered in the design of solar energy collectors, where it was useful to know the surface temperature of the collector plate in evaluating the effectiveness of the solar collection system.  Designers at Levelton Consultants Ltd. thought that it would be useful to characterize the effects of solar heating, independent of whatever was being heated.  A concept known as sol-air temperature was used to characterize the “effective” temperature of the air just above the surface, which took into account the effect of solar heating.  From there, one could figure in the effect of local wind and geometry to predict surface temperature.

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The calculation of sol-air temperature was based on a theoretical energy balance, which accounted for heat flows to and from the surface. This was done because, in the strictest sense, you couldn’t involve the surface itself or you would then have to account for heat transfer between the surface and whatever was under that surface, which would mean that the sol-air temperature could not be calculated independent of the surface itself. So they separated the two, and came up with a fictitious intermediate temperature that ignores the building under the roof assembly.

As it happens, engineers don’t really like fictitious temperatures. So when the Roofing Contractors Association of British Columbia (RCABC) asked Levelton to come up with a way to predict the effects of solar heating for a given location and roof system, they thought that the sol-air temperature would be just the thing, if they modified it to represent a “real” temperature. In fact, they suggested that one could use the sol-air temperature as a direct predictor of surface temperature, as they suspected that an insulated roof (nominally R28 or R40, say) would experience relatively little heat transfer between the surface of the roof and the building under it.

For portability and simplicity, the sol-air calculation tool was developed as a spreadsheet application. A quick calculation was desired, but a single instantaneous calculation was not considered to be useful. Monthly or annual results would produce a large amount of output data that would be confusing, and would slow down the calculation, so a diurnal temperature profile was determined to be the most useful form of output.

screen capture solair calculator


Figure 1: Screen capture from sol-air temperature calculator.




Comparison to Monitored Data

Levelton installed monitoring systems on several metal roof systems in Vancouver and Whistler. The direction, location and surface type of the roof systems varied, but the measured maximum surface temperatures are compared with the computed values in the following table: comparison data_Page_2



The only agreement in the above cases occurs on the north panel of a roof in Vancouver, which happens to be insulated (all other panels in the above table were uninsulated metal roofs above vented attic space). This underlines a key aspect of sol-air temperature: it is a surface effect only, and its development ignores heat transfer from the surface to the underlying structure.

Comparison to Calculated Data

The hypothesis that an insulated assembly would be an appropriate subject for sol-air analysis was tested by comparing results from the sol-air calculator with more detailed finite-volume models of assemblies of interest.

A copper-clad roof was investigated to estimate expected surface temperature under sunlit conditions. This roof had been leaking and was to be repaired. The existing assembly relied on the copper sheeting for waterproofing, and the many joints and seams in the roofing panels provided several potential avenues for leaks. The preferred repair would install a waterproofing membrane, but as a heritage assembly, the exterior appearance of the roof was to be maintained. The proposed solution was to install a self-adhered membrane covered with copper cladding, but solar heating on the metal surface could heat the surface above the service temperature of the self-adhered membrane. The result could be softening of the adhesive mastic behind the self-adhered membrane, or melting of the membrane itself. The sol-air calculator predicted a surface temperature of 91.2°C, and the finite-volume calculation predicted 96.8°C, within a reasonable level of accuracy. Thus, Levelton had some confidence that the expected surface temperature of this roof would exceed 90°C. As a consequence, they specified a high-temperature self-adhered membrane for this application, with a softening temperature of over 110°C (rather than the standard membrane that softens at 60°C).


Thus, the insulated roof approximates the condition of an adiabatic assembly, and therefore the sol-air analysis is suitable for this condition. It doesn’t work well for an uninsulated assembly, but the result actually overpredicts surface temperature, which is a conservative result so one could use it in that case as well. Where sol-air calculation is appropriate, it provides a simple tool to estimate surface temperatures without the need for detailed and complex computer modelling. This tool can be used with some confidence to predict the effect of solar heating on surface temperatures of insulated assemblies during the service life of the system. It would be possible to expand the sol-air tool to include nighttime cooling, or locations other than British Columbia, but that was beyond the scope of the investigation upon which this paper is based.

About the author: Alex McGowan, P.Eng., is Vice-President, Technical Services at Levelton Consultants Ltd. The above was excerpted from his paper: “A Practical Design Tool to Predict Surface Temperature in Solar Heating: Theory, Practice and Case Studies”.

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